function [q_up] = q_upperbar_proportional(k, Abar ,options)
% Provides the log(q_up)
%   Detailed explanation goes here
if isempty(options)
    options = optimoptions('fsolve','Display','off','OptimalityTolerance',1e-12);
end
q_up = fsolve(@(x) (k-1+(x-log(Abar)+1)*(Abar/exp(x))),log(Abar),options);

%k_fun = @(qup) 1 - (qup - log(Abar)+1)*exp(log(Abar)-qup);

end
